Overview of Real-Time Scheduling

Real-Time and Embedded Systems (M) Lecture 3

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d. Lecture Outline

•  Overview of real-time scheduling algorithms –  Clock-driven –  Weighted round-robin –  Priority-driven

•  Dynamic vs. static •  Deadline scheduling: EDF and LST •  Validation

•  Outline relative strengths, weaknesses

Material corresponds to chapter 4 of Liu’s book

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d. Approaches to Real-Time Scheduling

Different classes of scheduling algorithm used in real-time systems: •  Clock-driven

–  Primarily used for hard real-time systems where all properties of all jobs are known at design time, such that offline scheduling techniques can be used

•  Weighted round-robin –  Primarily used for scheduling real-time traffic in high-speed, switched

networks

•  Priority-driven –  Primarily used for more dynamic real-time systems with a mix of time-

based and event-based activities, where the system must adapt to changing conditions and events

Look at the properties of each in turn…

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d. Clock-Driven Scheduling

•  Decisions about what jobs execute when are made at specific time instants –  These instants are chosen before the system begins execution –  Usually regularly spaced, implemented using a periodic timer interrupt

•  Scheduler awakes after each interrupt, schedules the job to execute for the next period, then blocks itself until the next interrupt

•  E.g. the helicopter example with an interrupt every 1/180th of a second

•  E.g. the furnace control example, with an interrupt every 100ms

•  Typically in clock-driven systems: –  All parameters of the real-time jobs are fixed and known –  A schedule of the jobs is computed off-line and is stored for use at run-

time; as a result, scheduling overhead at run-time can be minimized –  Simple and straight-forward, not flexible

[Will discuss in more detail in lecture 4]

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d.

•  Regular round-robin scheduling is commonly used for scheduling time-shared applications –  Every job joins a FIFO queue when it is ready for execution –  When the scheduler runs, it schedules the job at the head of the queue to

execute for at most one time slice •  Sometimes called a quantum – typically O(tens of ms)

–  If the job has not completed by the end of its quantum, it is preempted and placed at the end of the queue

–  When there are n ready jobs in the queue, each job gets one slice every n time slices (n time slices is called a round)

–  Only limited use in real-time systems

Weighted Round-Robin Scheduling

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d. Weighted Round-Robin Scheduling

•  In weighted round robin each job Ji is assigned a weight wi; the job will receive wi consecutive time slices each round, and the duration of a round is

–  Equivalent to regular round robin if all weights equal 1 –  Simple to implement, since it doesn’t require a sorted priority queue

•  Partitions capacity between jobs according to some ratio •  Offers throughput guarantees

–  Each job makes a certain amount of progress each round

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wii=1

n∑

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d. Weighted Round-Robin Scheduling

•  By giving each job a fixed fraction of the processor time, a round-robin scheduler may delay the completion of every job –  A precedence constrained job may be assigned processor time, even while

it waits for its predecessor to complete; a job can’t take the time assigned to its successor to finish earlier

–  Not an issue for jobs that can incrementally consume output from their predecessor, since they execute concurrently in a pipelined fashion

•  E.g. Jobs communicating using Unix pipes •  E.g. Wormhole switching networks, where message transmission is carried out

in a pipeline fashion and a downstream switch can begin to transmit an earlier portion of a message, without having to wait for the arrival of the later portion

•  Weighted round-robin is primarily used for real-time networking; will discuss more in lecture 16

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d. Priority-Driven Scheduling

•  Assign priorities to jobs, based on some algorithm •  Make scheduling decisions based on the priorities, when events

such as releases and job completions occur –  Priority scheduling algorithms are event-driven –  Jobs are placed in one or more queues; at each event, the ready job with the

highest priority is executed –  The assignment of jobs to priority queues, along with rules such a whether

preemption is allowed, completely defines a priority scheduling algorithm

•  Priority-driven algorithms make locally optimal decisions about which job to run –  Locally optimal scheduling decisions are often not globally optimal –  Priority-driven algorithms never intentionally leave any resource idle

•  Leaving a resource idle is not locally optimal

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d. Example: Priority-Driven Scheduling

•  Consider the following task: –  Jobs J1, J2, …, J8, where Ji had higher priority than Jk if i < k

–  Jobs are scheduled on two processors P1 and P2 –  Jobs communicate via shared memory, so communication cost is negligible –  The schedulers keep one common priority queue of ready jobs –  All jobs are preemptable; scheduling decisions are made whenever some

job becomes ready for execution or a job completes

J5 4/2

J1 0/3

J2 0/1 J3 0/2 J4 0/2

J6 0/4

J7 0/4 J8 0/1

Release time

Execution time

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d. Example: Priority-Driven Scheduling

Time Not yet released

Released but not yet ready to run

Ready to run P1 P2 Completed

0

1

2

3

4

5

6

7

8

9

10

11

12 J5 4/2

J1 0/3

J2 0/1 J3 0/2 J4 0/2

J6 0/4

J7 0/4 J8 0/1

Release time

Execution time

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d. Example: Priority-Driven Scheduling

•  Note: The ability to preempt lower priority jobs slowed down the overall completion of the task –  This is not a general rule, but shows that priority scheduling results can be

non-intuitive –  Different priority scheduling algorithms can have very different properties

•  Tracing execution of jobs using tables is an effective way to demonstrate correctness for systems with periodic tasks and fixed timing constraints, execution times, resource usage –  Show that the system enters a repeating pattern of execution, and each

hyper-period of that pattern meets all deadlines –  Proof by exhaustive simulation

•  Provided the system has a manageably small number of jobs

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d.

•  Most scheduling algorithms used in non real-time systems are priority-driven –  First-In-First-Out –  Last-In-First-Out –  Shortest-Execution-Time-First –  Longest-Execution-Time-First

•  Real-time priority scheduling assigns priorities based on deadline or some other timing constraint: –  Earliest deadline first –  Least slack time first –  Etc.

Assign priority based on release time

Assign priority based on execution time

Priority-Driven Scheduling

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d. Priority Scheduling Based on Deadlines

•  Earliest deadline first (EDF) –  Assign priority to jobs based on deadline –  Earlier the deadline, higher the priority –  Simple, just requires knowledge of deadlines

•  Least Slack Time first (LST) –  A job Ji has deadline di, execution time ei, and was released at time ri –  At time t < di:

•  Remaining execution time trem = ei - (t - ri) •  Slack time tslack = di - t - trem

–  Assign priority to jobs based on slack time, tslack –  The smaller the slack time, the higher the priority –  More complex, requires knowledge of execution times and deadlines

•  Knowing the actual execution time is often difficult a priori, since it depends on the data, need to use worst case estimates (⇒ poor performance)

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d. Optimality of EDF and LST

•  These algorithms are optimal –  i.e. they will always produce a feasible schedule if one exists –  Constraints: on a single processor, as long as preemption is allowed and

jobs do not contend for resources

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d.

1.  Any feasible schedule can be transformed into an EDF schedule •  If Ji is scheduled to execute before Jk, but Ji’s deadline is later than Jk’s either:

•  The release time of Jk is after the Ji completes ⇒ they’re already in EDF order •  The release time of Jk is before the end of the interval in which Ji executes:

•  Swap Ji and Jk (this is always possible, since Ji’s deadline is later than Jk’s)

•  Move any jobs following idle periods forward into the idle period

⇒ the result is an EDF schedule

2.  So, if EDF fails to produce a feasible schedule, no feasible schedule exists •  If a feasible schedule existed it could be transformed into an EDF schedule,

contradicting the statement that EDF failed to produce a feasible schedule [Proof for LST is similar]

Optimality of EDF and LST: Proof

Ji Jk

dk di rk

Ji Jk Jk

Jk Ji Jk

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d. Non-Optimality of EDF and LST

•  Neither algorithm is optimal if jobs are non-preemptable or if there is more than one processor –  The book has examples which demonstrate EDF and LST producing

infeasible schedules in these cases •  This includes non-strict LST scheduling

–  Proof-by-counterexample

•  EDF and LST are simple priority-driven scheduling algorithms; introduced to show how we can reason about such algorithms –  Lectures 5-8 discuss other priority-driven scheduling algorithms

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d. Dynamic vs. Static Systems

•  If jobs are scheduled on multiple processors, and a job can be dispatched from the priority run queue to any of the

processors, the system is dynamic •  A job migrates if it starts execution on one processor and is

resumed on a different processor •  If jobs are partitioned into subsystems, and each subsystem is

bound statically to a processor, we have a static system •  Expect static systems to have inferior performance (in terms of

overall response time of the jobs) relative to dynamic systems –  But it is possible to validate static systems, whereas this is not always true

for dynamic systems –  For this reason, most hard real time systems are static

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d. Effective Release Times and Deadlines

•  Sometimes the release time of a job may be later than that of its successors, or its deadline may be earlier than that specified for its predecessors

•  This makes no sense: derive an effective release time or effective deadline consistent with all precedence constraints, and schedule using that –  Effective release time

•  If a job has no predecessors, its effective release time is its release time •  If it has predecessors, its effective release time is the maximum of its release

time and the effective release times of its predecessors –  Effective deadline

•  If a job has no successors, its effective deadline is its deadline •  It if has successors, its effective deadline is the minimum of its deadline and

the effective deadline of its successors

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d. Effective Release Times and Deadlines

•  Note: definition of effective deadline does not take into account execution time of successor jobs –  Would be more accurate, and needs to be done on multiprocessor systems –  But: unnecessary on single processor with preemptable jobs

–  Feasible to schedule any set of jobs according to their actual release times and deadline, iff feasible to schedule according to effective release times and deadlines

•  Ignore precedence constraints, schedule using effective release times and deadlines as if all jobs independent

•  Resulting schedule might meet deadlines but not precedence constraints –  If so, always possible to swap order of jobs within the schedule to meet deadlines

and precedence constraints

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d. Validating Priority-Driven Scheduling

•  Priority-driven scheduling has many advantages over clock-driven scheduling –  Better suited to applications with varying time and resource requirements,

since needs less a priori information –  Run-time overheads are small

•  But not widely used until recently, since difficult to validate –  Scheduling anomalies can occur for multiprocessor or non-preemptable

systems, or those which share resources •  Reducing the execution time of a job in a task can increase the total response

time of the task (see book for example) •  Not sufficient to show correctness with worse-case execution times, need to

simulate with all possible execution times for all jobs comprising a task –  Can be proved that anomalies do not occur for independent, preemptable,

jobs with fixed release times executed using any priority-driven scheduler on a single processor

•  Various stronger results exist for particular priority-driven algorithms

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d. Summary

•  Have outlined different approaches to scheduling: –  Clock-driven –  Weighted round-robin –  Priority-driven

and some of their constraints

•  Next session will be a tutorial to review the material covered to date, before we move onto detailed discussion of scheduling

•  Problem set 1 now available: due at 1:00pm on 25th January